Triangular Distribution Generator (min/mode/max)

What is a triangular distribution?

The triangular distribution models uncertainty when you can specify min, most likely (mode), and max values. It’s commonly used for quick estimates and PERT-like inputs.

a: minimum (optimistic).
c: mode / most likely value.
b: maximum (pessimistic).
If c is closer to a or b, the distribution becomes skewed.

PDF: for a≤x<c, 2(x-a)/((b-a)(c-a)); for c≤x≤b, 2(b-x)/((b-a)(b-c)). Mean: (a+b+c)/3. Variance: (a²+b²+c²-ab-ac-bc)/18.

You don’t need to enter personal information to use this tool.

Presets

Quickly set common estimation shapes (you can tweak values after applying).

Generator

Set min/mode/max, sample size, bins, and RNG. Then generate samples and export results.

Distribution

Sample size (N) Bins

RNG

Show theoretical PDF

Sample stats

Samples (first 20)

How to use this tool effectively

This guide helps you use Triangular Distribution Generator & Visualizer in a repeatable way: define a baseline, change one variable at a time, and interpret outputs with explicit assumptions before you share or act on results.

How it works

The page applies deterministic logic to your inputs and shows rounded output for readability. Treat it as a comparison workflow: run one baseline case, adjust a single parameter, and measure both absolute and percentage deltas. If a result seems off, verify units, time basis, and sign conventions before drawing conclusions. This approach keeps your analysis reproducible across teammates and sessions.

When to use

Use this page when you need a fast estimate, a classroom check, or a practical what-if comparison. It works best for planning and prioritization steps where you need direction and magnitude quickly before investing in deeper modeling, manual spreadsheets, or formal external review.

Common mistakes to avoid

Changing multiple parameters at once, which hides the true cause of output movement.
Mixing units (percent vs decimal, monthly vs yearly, gross vs net) across scenarios.
Comparing with another tool without aligning defaults, constants, and rounding rules.
Using rounded display values as exact downstream inputs without re-checking precision.

Interpretation and worked example

Run a baseline scenario and keep that result visible. Next, modify one assumption to reflect your realistic alternative and compare direction plus size of change. If the direction matches your domain expectation and the size is plausible, your setup is usually coherent. If not, check hidden defaults, boundary conditions, and interpretation notes before deciding which scenario to adopt.

FAQ

What do a, c, and b mean?

a is the minimum, c is the mode (most likely), and b is the maximum. They are often used as optimistic / most likely / pessimistic inputs.

What happens if c is not centered?

The distribution becomes skewed. If c is closer to a, it piles up more near the minimum; if c is closer to b, it piles up more near the maximum.

Is seeded RNG secure?

No. Seeded mode is for reproducibility only. Use Secure (CSPRNG) for security-sensitive randomness.

What should I do first on this page?

Start with the minimum required inputs or the first action shown near the primary button. Keep optional settings at defaults for a baseline run, then change one setting at a time so you can explain what caused each output change.

Why does this page differ from another tool?

Different pages often use different defaults, units, rounding rules, or assumptions. Align those settings before comparing outputs. If differences remain, compare each intermediate step rather than only the final number.

How to use Triangular Distribution Generator & Visualizer effectively

How this tool helps

Tools are designed for quick scenario comparisons. They work best when you keep one question per run, define success criteria first, and avoid switching objectives mid-stream. This reduces decision noise and produces results you can defend in follow-up review.

Input validation checklist

Before running, verify that required values are in the right format, that optional flags are intentionally set, and that baseline assumptions reflect current conditions. Invalid assumptions are often mistaken for tool bugs, so validation is part of interpretation quality.

Scenario planning pattern

Build three rows: conservative, expected, and aggressive cases. Keep data sources transparent for each case and compare output spacing. The pattern helps you spot non-linear jumps and decide whether a model is stable under plausible variation.

When to revisit inputs

Revisit inputs when input scale changes, time window shifts, or downstream decisions add new constraints. If constraints change, your previous output remains a useful reference but should not be treated as final guidance.

Operational checkpoint 1

Record the exact values and intent before you finalize any comparison. Confirm the unit system, date context, and business constraints. Compare outputs side by side and check whether differences are explained by one changed variable or by hidden assumptions. This checkpoint often reveals the single factor that changed everything.

Operational checkpoint 2